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Differentiate y=e^(x^2+2x)

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx. If we say u=(x 2 +2x) and therefore y=e u Then du/dx=2x+2 and dy/du=e u. Then dy/du*du/dx= (2x+2)e u , then we can s...
DF
Answered by Duncan F. • Maths tutor
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How do you differentiate 2^x?

We can differentiate this implicitly by writing the question as:y = 2 x Then we take the log of both sides:ln(y) = ln(2 x )Using the rules of logartithms this can be written as:ln(y) = x ln(2)Now we can diff...
AC
Answered by Alex C. • Maths tutor
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differentiate y=(4x^3)-5/x^2

to differentiate this equation we have to do it in two parts because there is a minus sign seperating them in the middle for the first part we first have to multiple the constant by what the power of x is wh...
GK
Answered by George K. • Maths tutor
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What is an easy way to remember how sin(x) and cos(x) are differentiated and integrated?

If you imagine that sin(x), cos(x), -sin(x) and -cos(x) are on a wheel as shown below: sin(x) -cos(x) cos(x) -sin(x) then going clockwise around the wheel you have what each term differentiates to, so sin(x)...
HE
Answered by Hannah E. • Maths tutor
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It is given f(x)=(19x-2)/((5-x)(1+6x)) can be expressed A/(5-x)+B/(1+6x) where A and B are integers. i) Find A and B ii) Show the integral of this from 0 to 4 = Kln5

Firstly, we are given that f(x) can be expressed in the above form, so we write this out: (19x-2)/((5-x)(1+6x)=A/(5-x)+B/(1+6x) We then multiply by the denominator of f(x): 19x-2=A(1+6x)+B(5-x) Now we can ch...
MW
Answered by Mike W. • Maths tutor
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